I think the fact of this suit is a good thing. First, I think it's pretty much impossible for these groups to win their case. SPLC is a private organization. The term "hate group" is a notion with a nebulous definition, so declaring it is falsely associated with the plaintiffs will be a difficult stretch. It's like suing someone for calling you an "asshole"--there's no way to win because there's no way to prove you're not an asshole. "Asshole" doesn't mean anything particular enough to define.

This will undoubtedly give the SPLC a chance to repeat the evil things it says these groups are doing and saying--the things that got them the "hate group"
designation in the first place.

There are lots of religious organizations who disagree with same-sex marriage and who disapprove of homosexual conduct who are not designated hate groups: the Roman Catholic Church, various protestant denominations. I suspect that these groups have done more than repeat Biblical passages or enacting catechisms that disapprove of same-sex relations.

Lively is best known for co-authoring, with Kevin Abrams, The Pink Swastika: Homosexuality in the Nazi Party. The book makes a series of claims that virtually no serious historian agrees with: that Hitler was gay, that “the Nazi Party was entirely controlled by militaristic homosexuals,” and that gays were especially selected for the SS because of their innate brutality. The claims are entirely false; in fact, the Nazis murdered significant numbers of gays and made homosexuality a death penalty offense in 1942. In the foreword, Abrams adds that homosexuality is “primarily a predatory addiction striving to take the weak and unsuspecting down with it. … They have no idea of how to act in the best interests of their country… . Their intention is to serve none but themselves.”

I'm pretty sure those claims go beyond Biblical injunctions against homosexual behavior. Here's more about the propaganda he uses the contributions of others to support:

In a 2007 open letter to the Russian people, he asserted that “homosexuality is a personality disorder that involves various, often dangerous sexual addictions and aggressive, anti-social impulses.” In 2009, he went to Uganda to speak at a major conference on the evils of homosexuality, saying, among other things: “The gay movement is an evil institution. The goal of the gay movement is to defeat the marriage-based society and replace it with a culture of sexual promiscuity.”

What's in the bold is false. The term "personality disorder" comes from psychology, a science that is not mentioned in the Bible, and the definitions of "personality disorder" appear in the DSM, not a theological text. Using a theological pretext to justify a medical claim is patently ridiculous. This is not legally sustainable.

Lively is perfectly within his rights to say such things. He cannot use his religion as a defense against legitimate attacks against him for saying these things, however.

More from my link, this time about a director at the American Family Association:

Fischer claimed in a blog post last May 27 that “[h]omosexuality gave us Adolph Hitler, and homosexuals in the military gave us the Brown Shirts, the Nazi war machine and 6 million dead Jews.” (Ironically, the elder Wildmon was widely denounced as an anti-Semite after suggesting that Jews control the media, which the AFA says “shows a genuine hostility towards Christians.”) Fischer has described Hitler as “an active homosexual” who sought out gays “because he could not get straight soldiers to be savage and brutal and vicious enough.” He proposed criminalizing homosexual behavior in another 2010 blog post and has advocated forcing gays into “reparative” therapy.

Again, these are false claims that tend to make people hate a particular group of people. They are not Biblical in nature. How can someone claim a religious exemption for this?

Jerry Boykin of the Family Research Council, an organization once attacked by a man convicted as a domestic terrorist because they were included on the SPLC Hate Map, said, “The Southern Poverty Law Center is reckless in labeling groups as hate groups or labeling individuals as hate mongers, and they do both. They have no authority to do so.”

No authority? They don't need "authority." They need the first amendment.

DJKM is perfectly within its rights to say anything they like. And the SPLC is within its rights to denounce them for it. Speech versus speech. It's the American way.

If someone can label homosexuals as the authors of Nazism, as "savage and brutal," "dangerous sexual addiction," "aggressive," or "anti-social," why can't someone else label these statements "hate?" Everyone is allowed to make value judgments about others. No one is suing DJKM to make them stop saying these things--they are protected by the First Amendment.